Page 1 Geometry

WASHINGTON STATE
END-OF-COURSE EXAM

GEOMETRY PRACTICE TEST

Name: _________________________________________________

Date: __________________________________________________
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GENERAL DIRECTIONS
Today you will be taking a Washington State Geometry End-of-Course
Practice Test. To complete this test, you will need to use the answer
document provided with this practice test on page 22. This practice test
is designed to simulate the Washington State Geometry testing
experience.

Three different types of questions appear on this test:

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While taking this test, remember:

1. Read each question carefully, including diagrams and graphs.

2. For multiple-choice questions, choose the best answer from the

four choices given. Mark only one response for each multiple-
choice question.

3. For short-answer questions, write your answers in the box

provided. You do not have to use all of the space provided. Answers
may be graphs, text, or calculations.

4.If a short-answer question asks you to show your work, you must
do so to receive full credit. If you are using a calculator, describe
the calculation process you used in enough detail to be
duplicated, including the numbers you entered and the function
keys you pressed to find the answer. If a short-answer item has
multiple parts, label each section of work and clearly identify your
answer for each part.

A formula sheet is provided for the Geometry End-of-Course Exam, and is

provided on Page 20 and 21 of this Practice Test.

The Practice Test will be broken up into 3 different sections and will be
completed in one sitting that will last approximately 150 minutes (there
is no time limit):

Section 1: Questions 1-6

* Logical arguments and proof

Section 2: Questions 7-29

* Proving and applying properties of 2-dimensional figures

Section 3: Questions 30-37

* Figures in a coordinate plane and measurement
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* Be sure to answer all questions before you end each test session.
However, do not spend too much time on any one question.

* If you do not know the answer to a question, make your best guess and
go on to the next question.

* You will not be penalized for guessing.

GEOMETRY END-OF-COURSE EXAM: PRACTICE TEST

1. Seth was supposed to prove €ABC ≅ ΔPQR by SAS for his homework assignment. He
wrote the following proof:

Given € ABC ≅ ∠PRQ , AB ≅ PQ , and BC ≅ QR , then €ABC ≅ ΔPQR by

SAS. €

Which statement should

€ be changed in €
order for Seth’s proof to be correct?
€a. € ABC ≅ ∠PRQ should be rewritten as € ABC€ ≅ ∠PQR .
b. AB ≅ PQ should be rewritten as AB ≅ PR .
c. BC ≅ QR should be rewritten as AC ≅ QR .
€ € be rewritten as €ABC ≅ ΔPQR by SSA.
d. €ABC ≅ ΔPQR by SAS should
€
€
€ €

€2. Which of the following best describes a counterexample

€ to the assertion below:

Two lines in a plane always intersect in exactly one point.

a. Coplanar Lines
b. Intersecting Lines
c. Parallel Lines
d. Perpendicular Lines

3. Which of the following statements is true:

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a. A postulate is a proven fact using theorems, definitions, and undefined terms.

b. A theorem is a proven fact using postulates, definitions, and undefined terms.
c. Some defined geometric terms are line, plane, and point.
d. Some undefined geometry terms are angle, ray, and line segment.

4. Given: € CBF ≅ ∠CDG , AC bisects € BAD .

Prove: AD ≅ AB

€
€€ €
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5. If an indirect proof is used to prove the following theorem, then which assumption must be
proved false?
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If two lines form a pair of congruent corresponding angles, then the lines are
parallel.

a. The corresponding angles are congruent.

b. The corresponding angles are not congruent.
c. The lines intersect.
d. The lines do not intersect.

6. Given the statement:

Conditional: If the table top is rectangular, then its diagonals are congruent.

The inverse of the conditional statement is:

Inverse: If the diagonals of a table top are congruent, then it is rectangular.

Identify by writing yes/no on the first line below if the statement above has correctly
identified the inverse of the conditional. If the inverse above is incorrect, correctly write it
in the space below.

Inverse of Conditional

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7. What is the name of the point of concurrency where the three angle bisectors of a triangle
meet?
a. Circumcenter
b. Incenter
c. Centroid
d. Orthocenter

8. Given that €ABC ≅ ΔDEC and m∠E = 23° , find m∠ACB .

€ € €

a. m∠ACB = 77°
b. m∠ACB = 67°
c. m∠ACB = 23°
€ d. m∠ACB =113°
€
€
9. Triangle JKE is an obtuse isosceles triangle with m∠E =10° and KE > JK.
€
What is the measure of m∠J ?
a. 170°
€
b. 160°
c. 85°
€
€ d. 10°
€
€
€
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10. In the diagram:

AB ≅ EB
∠ADB ≅ ∠ECB

Prove €ABD ≅ ΔEBC using mathematical language and concepts.

€
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11. Choose the true statement based on knowing point O is the orthocenter of triangle ABC.

a. € BDA ≅ ∠CDA
b. BO ≅ CO

c. € BAD ≅ ∠CAD
€
€ d. EO ≅ FO

€
€

12. Which triangles are congruent in the diagram?

a. HMN  HGN
b. HMN  NGH
c. NMH  NGH
d. MNH  HGN

13. Find the length of side TV.

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a. 11
b. 11 2
c. 11 3

€ €
d. 22
€

€
14. A tree casts a shadow that is 150 feet long. If the angle of elevation from the tip of the
shadow to the top of the tree is
30°, how tall is the tree to the
nearest foot?

a. 87 feet
b. 106 feet
c. 212 feet
d. 259 feet

15. A rectangular prism is shown. The base of the prism is a square. The length of the diagonal
from top corner A to opposite bottom corner B is 2 feet.
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Determine the exact length of the box in inches.

Write your answer on the line.

What is the exact length of the box? _______________ inches

16. Which side lengths represent the sides of a right triangle?

a. 1, 1, 2
b. 2, 3, 5
c. 5, 12, 13
d. 7, 23, 25

17. Use the trigonometric ratio sin A = 0.38 to

determine which angle of the triangle is € A .
a. €2
€
€
€
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b. €1
c. €3
d. No Solution

€
€
18. Find the value of y.
a. y = 5sin28°
b. y = 5 cos28°
c. y = 5cos62°
€
d. y = 5sin62°
€
€
€

19. At takeoff, a plane flies at an angle of 10° with the runway. After it has traveled a ground
distance of 2,800 feet, find the vertical distance the plane has gained from takeoff. Round
your answer to the nearest foot.
a. 486 feet
b. 494 feet
c. 2,757 feet
d. 15,880 feet

20. In parallelogram PQRS the measures of angle P and angle R are each 146. What is the
measure of angle Q?
a. 146
b. 112
c. 68
d. 34

21. Which statement can you use to conclude that

quadrilateral XYZW is a parallelogram?

a. XW ≅ YZ and  XY ≅ WZ

€
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b. XW ≅ WZ and  XY ≅ WZ
c. YN ≅ NX and  XN ≅ NY
d. XW ≅ YZ and  XY ≅ YZ
€
€
€
22. Which description does NOT guarantee that a quadrilateral is a parallelogram?
a. A quadrilateral with both pairs of opposite sides congruent.
b. A quadrilateral with the diagonals bisecting each other.
c. A quadrilateral with consecutive angles supplementary.
d. Quadrilateral with two opposite sides parallel.

23. In the following polygon, determine the value of x.

a. 78
b. 81
c. 95
d. 99

24. One exterior angle of a regular polygon measures 97°. What is the measure of one interior
angle?
a. 7
b. 83
c. 173
d. 263

25. What is the missing reason for the proof?

Given: Parallelogram ABCD with diagonal BD

Prove: €ABD ≅ ΔCDB

€
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a. Reflexive Property of Congruence

b. ASA
c. Alternative Interior Angles Theorem
d. SSS

26. In the accompanying diagram of rectangle ABCD, m∠ABE = 30 and m∠CFE = 144. Find
m∠BEF.

a. 36°
b. 60°
c. 84°
d. 90°

27. In trapezoid DEFG, find

m∠D .
a. 44
b. 72
c. 108
d. 136
€
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28. Which of the following statements is always true of any rhombus ABCD?

a. € A ≅ ∠B
b. AB⊥BC
c. AC ≅ BD
€
d. AC⊥BD
€€

€
29. In kite DEFC, if m∠DCF = 20 and m∠DEF = 80 , find
m∠CDE .

€ €
€
Write your answer on the line below

m∠CDE = _____________________________________________

30. The vertices of a square are (3, 1), (-2, 0), (-1, -5), and (4, -4). The diagonals of the square
intersect at point Q.
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Determine the coordinates of point Q.

You may use the blank grid to help determine the solution.

Write your answer on the line.

What are the coordinates of point Q? ( ______, ______ )

31. Isosceles triangle ABC has vertices at A(0, 0), B(8, 0), and C(x, 12).

The value of x could be:

a. 4
b. 8
c. 12
d. 16

32. What is the most precise name for a quadrilateral with vertices (-4, -1), (1, -1), (4, 3), and
(-1, 3)?
a. Kite
Page 18 Geometry

b. Parallelogram
c. Trapezoid
d. Rhombus

33. The U.S. Census Bureau reported a national population of 299,894,924 on its Population
Clock in mid-October of 2006. One can say that the U.S. population is 3 hundred million
(3 x 108) and be precise to one digit. Although the population had surpassed 3 hundred
million by the end of that month explain why 3 x 108 remained precise to one digit.

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34. What is the best estimate for the surface area of the prism?
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a. 34 ft2
b. 48 ft2
c. 72 ft2
d. 96 ft2

35. Convert 20 miles/hour to meters/second (round to the nearest meter).

1 mile = 5,280 feet
1 foot = .3048 meters

Write your answer on the line below.

20 miles/hour = ______________ meters/second

36. There are 5 horses on 12 acres of land. What is the mean number of square yards per horse?
Page 20 Geometry

1 acre = 43,560 square feet

a. 8,712 square yards
b. 11,616 square yards
c. 34,848 square yards
d. 58,080 square yards

37. On a coordinate grid, a grocery store is located at (3,0) and the hardware store is located at
(4,3). If the hardware store is the midpoint between the grocery store and the pharmacy,
what is the approximate distance from the hardware store to the pharmacy? (Note: 1 unit
equals 1 mile)
a. 1.5 miles
b. 1.58 miles
c. 3.16 miles
d. 3.5 miles
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NAME: ___________________________________________
GEOMETRY END-OF-COURSE EXAM PRACTICE TEST
Answer Key
Problem Problem
Answer Standard Answer Standard
Number Number
1 G.1.E 20 G.3.F

2 G.1.E 21 G.3.F

3 G.1.E 22 G.3.F

4 G.1.C 23 G.3.G

5 G.1.C 24 G.3.G

6 Short Answer G.1.D 25 G.3.G

7 G.3.A 26 G.3.G

8 G.3.A 27 G.3.G

9 G.3.A 28 G.3.G

10 Short Answer G.3.B 29 G.3.G

11 G.3.A 30 G.4.B

12 G.3.B 31 G.4.C

13 G.3.C 32 G.4.C

14 G.3.C 33 Short Answer G.6.E

15 G.3.D 34 G.4.E

16 G.3.D 35 G.6.F

17 G.3.E 36 G.6.F

18 G.3.E 37 G.6.F

19 G.3.E

SCALE SCORE: / 40
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Number of Items Total

Reporting
MC CP SA Number
Strands Total
(1-point) (1-point) (2-points) of Points
1. G.1.E 6. G.1.D
Logical 2. G.1.E
arguments and 3. G.1.F 6 7
proof 4. G.1.C
5. G.1.C
7. G.3.A 15. G.3.D 10. G.3.B
8. G.3.A 25. G.3.F
9. G.3.A 29. G.3.G
11. G.3.A
12. G.3.B
13. G.3.C
14. G.3.C
Proving and 16. G.3.D
applying 17. G.3.E
properties of 2- 18. G.3.E 23 24
dimensional 19. G.3.E
figures 20. G.3.F
21. G.3.F
22. G.3.F
23. G.3.G
24. G.3.G
26. G.3.G
27. G.3.G
28. G.3.G
31. G.4.C 30. G.4.B 33. G.6.E
Figures in a 32. G.4.C 35. G.6.F
coordinate
34. G.4.E 8 9
plane and
measurement 36. G.6.F
37. G.6.F
Total Items 29 5 3 37 40

GEOMETRY END-OF-COURSE EXAM PRACTICE

TEST MAP